# Copyright (C) 2022 Shichao Wu, Alex Nitz
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3 of the License, or (at your
# option) any later version.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# =============================================================================
#
# Preamble
#
# =============================================================================
#
"""
This module provides (semi-)analytical PSDs and sensitivity curves for space
borne detectors, such as LISA, Taiji, and TianQin. Based on LISA technical note
<LISA-LCST-SGS-TN-001>, LDC manual <LISA-LCST-SGS-MAN-001>,
paper <10.1088/1361-6382/ab1101>, <10.1088/0264-9381/33/3/035010>,
<10.1103/PhysRevD.102.063021>, <10.1103/PhysRevD.100.043003>,
and <10.1103/PhysRevD.107.064021>.
"""
import numpy as np
from scipy.interpolate import interp1d
from astropy.constants import c
from pycbc.psd.read import from_numpy_arrays
def _psd_acc_noise(f, acc_noise_level=None):
""" The PSD of TDI-based space-borne GW
detectors' acceleration noise. Note that
this is suitable for LISA and Taiji, TianQin
has a different form.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
Returns
-------
s_acc_nu : float or numpy.array
The PSD value or array for acceleration noise.
Notes
-----
Please see Eq.(11-13) in <LISA-LCST-SGS-TN-001> for more details.
"""
s_acc = acc_noise_level**2 * (1+(4e-4/f)**2)*(1+(f/8e-3)**4)
s_acc_d = s_acc * (2*np.pi*f)**(-4)
s_acc_nu = (2*np.pi*f/c.value)**2 * s_acc_d
return s_acc_nu
[docs]def psd_lisa_acc_noise(f, acc_noise_level=3e-15):
""" The PSD of LISA's acceleration noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
Returns
-------
s_acc_nu : float or numpy.array
The PSD value or array for acceleration noise.
Notes
-----
Please see Eq.(11-13) in <LISA-LCST-SGS-TN-001> for more details.
"""
s_acc_nu = _psd_acc_noise(f, acc_noise_level)
return s_acc_nu
[docs]def psd_tianqin_acc_noise(f, acc_noise_level=1e-15):
""" The PSD of TianQin's acceleration noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
Returns
-------
s_acc_nu : float or numpy.array
The PSD value or array for acceleration noise.
Notes
-----
Please see Table(1) in <10.1088/0264-9381/33/3/035010>
and that paper for more details.
"""
s_acc_d = acc_noise_level**2 * (2*np.pi*f)**(-4) * (1+1e-4/f)
s_acc_nu = (2*np.pi*f/c.value)**2 * s_acc_d
return s_acc_nu
[docs]def psd_taiji_acc_noise(f, acc_noise_level=3e-15):
""" The PSD of Taiji's acceleration noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
Returns
-------
s_acc_nu : float or numpy.array
The PSD value or array for acceleration noise.
Notes
-----
Please see Eq.(2) in <10.1103/PhysRevD.107.064021> for more details.
"""
s_acc_nu = _psd_acc_noise(f, acc_noise_level)
return s_acc_nu
def _psd_oms_noise(f, oms_noise_level=None):
""" The PSD of TDI-based space-borne GW detectors' OMS noise.
Note that this is suitable for LISA and Taiji, TianQin
has a different form.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
oms_noise_level : float
The level of OMS noise.
Returns
-------
s_oms_nu : float or numpy.array
The PSD value or array for OMS noise.
Notes
-----
Please see Eq.(9-10) in <LISA-LCST-SGS-TN-001> for more details.
"""
s_oms_d = oms_noise_level**2 * (1+(2e-3/f)**4)
s_oms_nu = s_oms_d * (2*np.pi*f/c.value)**2
return s_oms_nu
[docs]def psd_lisa_oms_noise(f, oms_noise_level=15e-12):
""" The PSD of LISA's OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
oms_noise_level : float
The level of OMS noise.
Returns
-------
s_oms_nu : float or numpy.array
The PSD value or array for OMS noise.
Notes
-----
Please see Eq.(9-10) in <LISA-LCST-SGS-TN-001> for more details.
"""
s_oms_nu = _psd_oms_noise(f, oms_noise_level)
return s_oms_nu
[docs]def psd_tianqin_oms_noise(f, oms_noise_level=1e-12):
""" The PSD of TianQin's OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
oms_noise_level : float
The level of OMS noise.
Returns
-------
s_oms_nu : float or numpy.array
The PSD value or array for OMS noise.
Notes
-----
Please see Table(1) in <10.1088/0264-9381/33/3/035010>
and that paper for more details.
"""
s_oms_d = oms_noise_level**2
s_oms_nu = s_oms_d * (2*np.pi*f/c.value)**2
return s_oms_nu
[docs]def psd_taiji_oms_noise(f, oms_noise_level=8e-12):
""" The PSD of Taiji's OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
oms_noise_level : float
The level of OMS noise.
Returns
-------
s_oms_nu : float or numpy.array
The PSD value or array for OMS noise.
Notes
-----
Please see Eq.(1) in <10.1103/PhysRevD.107.064021> for more details.
"""
s_oms_nu = _psd_oms_noise(f, oms_noise_level)
return s_oms_nu
[docs]def lisa_psd_components(f, acc_noise_level=3e-15, oms_noise_level=15e-12):
""" The PSD of LISA's acceleration and OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
low_freq_component, high_freq_component :
The PSD value or array for acceleration and OMS noise.
"""
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
low_freq_component = psd_lisa_acc_noise(f, acc_noise_level)
high_freq_component = psd_lisa_oms_noise(f, oms_noise_level)
return low_freq_component, high_freq_component
[docs]def tianqin_psd_components(f, acc_noise_level=1e-15, oms_noise_level=1e-12):
""" The PSD of TianQin's acceleration and OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
low_freq_component, high_freq_component :
The PSD value or array for acceleration and OMS noise.
"""
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
low_freq_component = psd_tianqin_acc_noise(f, acc_noise_level)
high_freq_component = psd_tianqin_oms_noise(f, oms_noise_level)
return low_freq_component, high_freq_component
[docs]def taiji_psd_components(f, acc_noise_level=3e-15, oms_noise_level=8e-12):
""" The PSD of Taiji's acceleration and OMS noise.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
low_freq_component, high_freq_component :
The PSD value or array for acceleration and OMS noise.
"""
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
low_freq_component = psd_taiji_acc_noise(f, acc_noise_level)
high_freq_component = psd_taiji_oms_noise(f, oms_noise_level)
return low_freq_component, high_freq_component
[docs]def omega_length(f, len_arm=None):
""" The function to calculate 2*pi*f*arm_length.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of LISA, TianQin, or Taiji. The default
value here is None.
Returns
-------
omega_len : float or numpy.array
The value of 2*pi*f*arm_length.
"""
omega_len = 2*np.pi*f * len_arm/c.value
return omega_len
def _analytical_psd_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm=None, psd_components=None, tdi=None):
""" The TDI-1.5/2.0 analytical PSD (X,Y,Z channel) for TDI-based
space-borne GW detectors.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of the detector, in the unit of "m".
psd_components : numpy.array
The PSDs of acceleration noise and OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel).
Notes
-----
Please see Eq.(19-20) in <LISA-LCST-SGS-TN-001> for more details.
"""
len_arm = np.float64(len_arm)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
s_acc_nu, s_oms_nu = psd_components
omega_len = omega_length(fr, len_arm)
psd = 16*(np.sin(omega_len))**2 * (s_oms_nu +
s_acc_nu*(3+np.cos(2*omega_len)))
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
psd *= tdi2_factor
fseries = from_numpy_arrays(fr, psd, length, delta_f, low_freq_cutoff)
return fseries
[docs]def analytical_psd_lisa_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12, tdi=None):
""" The TDI-1.5/2.0 analytical PSD (X,Y,Z channel) for LISA.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for LISA.
Notes
-----
Please see Eq.(19-20) in <LISA-LCST-SGS-TN-001> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(lisa_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_tianqin_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12, tdi=None):
""" The TDI-1.5/2.0 analytical PSD (X,Y,Z channel) for TianQin.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for TianQin.
Notes
-----
Please see Table(1) in <10.1088/0264-9381/33/3/035010>
for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(tianqin_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_taiji_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12, tdi=None):
""" The TDI-1.5/2.0 analytical PSD (X,Y,Z channel) for Taiji.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for Taiji.
Notes
-----
Please see <10.1103/PhysRevD.107.064021> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(taiji_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_XYZ(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
def _analytical_csd_tdi_XY(length, delta_f, low_freq_cutoff,
len_arm=None, psd_components=None, tdi=None):
""" The cross-spectrum density between TDI channel X and Y.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of the detector, in the unit of "m".
psd_components : numpy.array
The PSDs of acceleration noise and OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The CSD between TDI-1.5/2.0 channel X and Y.
Notes
-----
Please see Eq.(56) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
len_arm = np.float64(len_arm)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
s_acc_nu, s_oms_nu = psd_components
omega_len = omega_length(fr, len_arm)
csd = (-8*np.sin(omega_len)**2 * np.cos(omega_len) *
(s_oms_nu+4*s_acc_nu))
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
csd *= tdi2_factor
fseries = from_numpy_arrays(fr, csd, length, delta_f, low_freq_cutoff)
return fseries
[docs]def analytical_csd_lisa_tdi_XY(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12, tdi=None):
""" The cross-spectrum density between LISA's TDI channel X and Y.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The CSD between LISA's TDI-1.5/2.0 channel X and Y.
Notes
-----
Please see Eq.(56) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(lisa_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_csd_tdi_XY(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
def _analytical_psd_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm=None, psd_components=None, tdi=None):
""" The PSD of TDI-1.5/2.0 channel A and E.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of the detector, in the unit of "m".
psd_components : numpy.array
The PSDs of acceleration noise and OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of TDI-1.5/2.0 channel A and E.
Notes
-----
Please see Eq.(58) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
len_arm = np.float64(len_arm)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
s_acc_nu, s_oms_nu = psd_components
omega_len = omega_length(fr, len_arm)
psd = (8*(np.sin(omega_len))**2 *
(4*(1+np.cos(omega_len)+np.cos(omega_len)**2)*s_acc_nu +
(2+np.cos(omega_len))*s_oms_nu))
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
psd *= tdi2_factor
fseries = from_numpy_arrays(fr, psd, length, delta_f, low_freq_cutoff)
return fseries
[docs]def analytical_psd_lisa_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12, tdi=None):
""" The PSD of LISA's TDI-1.5/2.0 channel A and E.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of LISA's TDI-1.5/2.0 channel A and E.
Notes
-----
Please see Eq.(58) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(lisa_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_tianqin_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12, tdi=None):
""" The PSD of TianQin's TDI-1.5/2.0 channel A and E.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of TianQin's TDI-1.5/2.0 channel A and E.
Notes
-----
Please see Table(1) in <10.1088/0264-9381/33/3/035010>
for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(tianqin_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_taiji_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12, tdi=None):
""" The PSD of Taiji's TDI-1.5/2.0 channel A and E.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of Taiji's TDI-1.5/2.0 channel A and E.
Notes
-----
Please see <10.1103/PhysRevD.107.064021> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(taiji_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
def _analytical_psd_tdi_T(length, delta_f, low_freq_cutoff,
len_arm=None, psd_components=None, tdi=None):
""" The PSD of TDI-1.5/2.0 channel T.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of the detector, in the unit of "m".
psd_components : numpy.array
The PSDs of acceleration noise and OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of TDI-1.5/2.0 channel T.
Notes
-----
Please see Eq.(59) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
len_arm = np.float64(len_arm)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
s_acc_nu, s_oms_nu = psd_components
omega_len = omega_length(fr, len_arm)
psd = (32*np.sin(omega_len)**2 * np.sin(omega_len/2)**2 *
(4*s_acc_nu*np.sin(omega_len/2)**2 + s_oms_nu))
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
psd *= tdi2_factor
fseries = from_numpy_arrays(fr, psd, length, delta_f, low_freq_cutoff)
return fseries
[docs]def analytical_psd_lisa_tdi_T(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12, tdi=None):
""" The PSD of LISA's TDI-1.5/2.0 channel T.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of LISA's TDI-1.5/2.0 channel T.
Notes
-----
Please see Eq.(59) in <LISA-LCST-SGS-MAN-001(Radler)> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(lisa_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_T(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_tianqin_tdi_T(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12, tdi=None):
""" The PSD of TianQin's TDI-1.5/2.0 channel T.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of TianQin's TDI-1.5/2.0 channel T.
Notes
-----
Please see Table(1) in <10.1088/0264-9381/33/3/035010>
for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(tianqin_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_T(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def analytical_psd_taiji_tdi_T(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12, tdi=None):
""" The PSD of Taiji's TDI-1.5/2.0 channel T.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The PSD of Taiji's TDI-1.5/2.0 channel T.
Notes
-----
Please see <10.1103/PhysRevD.107.064021> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
psd_components = np.array(taiji_psd_components(
fr, acc_noise_level, oms_noise_level))
fseries = _analytical_psd_tdi_T(length, delta_f, low_freq_cutoff,
len_arm, psd_components, tdi)
return fseries
[docs]def averaged_lisa_fplus_sq_numerical(f, len_arm=2.5e9):
""" A numerical fit for LISA's squared antenna response function,
averaged over sky and polarization angle.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of LISA, in the unit of "m".
Returns
-------
fp_sq_numerical : float or numpy.array
The sky and polarization angle averaged squared antenna response.
Notes
-----
Please see Eq.(36) in <LISA-LCST-SGS-TN-001> for more details.
"""
from astropy.utils.data import download_file
if len_arm != 2.5e9:
raise ValueError("Currently only support 'len_arm=2.5e9'.")
# Download the numerical LISA averaged response.
url = "https://zenodo.org/record/7497853/files/AvFXp2_Raw.npy"
file_path = download_file(url, cache=True)
freqs, fp_sq = np.load(file_path)
# Padding the end.
freqs = np.append(freqs, 2)
fp_sq = np.append(fp_sq, 0.0012712348970728724)
fp_sq_interp = interp1d(freqs, fp_sq, kind='linear',
fill_value="extrapolate")
fp_sq_numerical = fp_sq_interp(f)/16
return fp_sq_numerical
[docs]def averaged_fplus_sq_approximated(f, len_arm=None):
r""" A simplified fit for TDI-based space-borne GW detectors'
squared antenna response function, averaged over sky and
polarization angle.
.. math::
<\left(F_{X}^{+}\right)^{2}>\approx \frac{3}{20} \frac{1}{
1+0.6(\omega L)^{2}}
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of the detector, in the unit of "m".
Returns
-------
fp_sq_approx : float or numpy.array
The sky and polarization angle averaged squared antenna response.
Notes
-----
Please see Eq.(9) in <10.1088/1361-6382/ab1101> for more details.
"""
fp_sq_approx = (3./20.)*(1./(1.+0.6*omega_length(f, len_arm)**2))
return fp_sq_approx
[docs]def averaged_tianqin_fplus_sq_numerical(f, len_arm=np.sqrt(3)*1e8):
""" A numerical fit for TianQin's squared antenna response function,
averaged over sky and polarization angle.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of TianQin, in the unit of "m".
Returns
-------
fp_sq_numerical : float or numpy.array
The sky and polarization angle averaged squared antenna response.
Notes
-----
Please see Eq.(15-16) in <10.1103/PhysRevD.100.043003>
for more details.
"""
base = averaged_fplus_sq_approximated(f, len_arm)
a = [1, 1e-4, 2639e-4, 231/5*1e-4, -2093/1.25*1e-4, 2173e-5,
2101e-6, 3027/2*1e-5, -42373/5*1e-6, 176087e-8,
-8023/5*1e-7, 5169e-9]
omega_len = omega_length(f, len_arm)
omega_len_low_f = omega_len[omega_len < 4.1]
omega_len_high_f = omega_len[omega_len >= 4.1]
base_low_f = base[:len(omega_len_low_f)]
base_high_f = base[len(omega_len_low_f):]
low_f_modulation = np.polyval(a[::-1], omega_len_low_f)
high_f_modulation = np.exp(
-0.322 * np.sin(2*omega_len_high_f-4.712) + 0.078
)
low_f_result = np.multiply(base_low_f, low_f_modulation)
high_f_result = np.multiply(base_high_f, high_f_modulation)
fp_sq_numerical = np.concatenate((low_f_result, high_f_result))
return fp_sq_numerical
[docs]def averaged_response_lisa_tdi(f, len_arm=2.5e9, tdi=None):
""" LISA's TDI-1.5/2.0 response function to GW,
averaged over sky and polarization angle.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of LISA, in the unit of "m".
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
response_tdi : float or numpy.array
The sky and polarization angle averaged TDI-1.5/2.0 response to GW.
Notes
-----
Please see Eq.(39-40) in <LISA-LCST-SGS-TN-001> for more details.
"""
omega_len = omega_length(f, len_arm)
ave_fp2 = averaged_lisa_fplus_sq_numerical(f, len_arm)
response_tdi = (4*omega_len)**2 * np.sin(omega_len)**2 * ave_fp2
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
response_tdi *= tdi2_factor
return response_tdi
[docs]def averaged_response_tianqin_tdi(f, len_arm=np.sqrt(3)*1e8, tdi=None):
""" TianQin's TDI-1.5/2.0 response function to GW,
averaged over sky and polarization angle.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of TianQin, in the unit of "m".
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
response_tdi : float or numpy.array
The sky and polarization angle averaged TDI-1.5/2.0 response to GW.
"""
omega_len = omega_length(f, len_arm)
ave_fp2 = averaged_tianqin_fplus_sq_numerical(f, len_arm)
response_tdi = (4*omega_len)**2 * np.sin(omega_len)**2 * ave_fp2
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
response_tdi *= tdi2_factor
return response_tdi
[docs]def averaged_response_taiji_tdi(f, len_arm=3e9, tdi=None):
""" Taiji's TDI-1.5/2.0 response function to GW,
averaged over sky and polarization angle.
Parameters
----------
f : float or numpy.array
The frequency or frequency range, in the unit of "Hz".
len_arm : float
The arm length of Taiji, in the unit of "m".
tdi : str
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
response_tdi : float or numpy.array
The sky and polarization angle averaged TDI-1.5/2.0 response to GW.
"""
omega_len = omega_length(f, len_arm)
ave_fp2 = averaged_fplus_sq_approximated(f, len_arm)
response_tdi = (4*omega_len)**2 * np.sin(omega_len)**2 * ave_fp2
if str(tdi) not in ["1.5", "2.0"]:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
if str(tdi) == "2.0":
tdi2_factor = 4*(np.sin(2*omega_len))**2
response_tdi *= tdi2_factor
return response_tdi
[docs]def sensitivity_curve_lisa_semi_analytical(length, delta_f, low_freq_cutoff,
len_arm=2.5e9,
acc_noise_level=3e-15,
oms_noise_level=15e-12):
""" The semi-analytical LISA's sensitivity curve (6-links),
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged semi-analytical
LISA's sensitivity curve (6-links).
Notes
-----
Please see Eq.(42-43) in <LISA-LCST-SGS-TN-001> for more details.
"""
len_arm = np.float64(len_arm)
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
fp_sq = averaged_lisa_fplus_sq_numerical(fr, len_arm)
s_acc_nu, s_oms_nu = lisa_psd_components(
fr, acc_noise_level, oms_noise_level)
omega_len = omega_length(fr, len_arm)
sense_curve = ((s_oms_nu + s_acc_nu*(3+np.cos(2*omega_len))) /
(omega_len**2*fp_sq))
fseries = from_numpy_arrays(fr, sense_curve/2,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_tianqin_analytical(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12):
""" The analytical TianQin's sensitivity curve (6-links),
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged analytical
TianQin's sensitivity curve (6-links).
"""
len_arm = np.float64(len_arm)
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
fp_sq = averaged_tianqin_fplus_sq_numerical(fr, len_arm)
s_acc_nu, s_oms_nu = tianqin_psd_components(
fr, acc_noise_level, oms_noise_level)
omega_len = omega_length(fr, len_arm)
sense_curve = ((s_oms_nu + s_acc_nu*(3+np.cos(2*omega_len))) /
(omega_len**2*fp_sq))
fseries = from_numpy_arrays(fr, sense_curve/2,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_taiji_analytical(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12):
""" The analytical Taiji's sensitivity curve (6-links),
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged analytical
Taiji's sensitivity curve (6-links).
"""
len_arm = np.float64(len_arm)
acc_noise_level = np.float64(acc_noise_level)
oms_noise_level = np.float64(oms_noise_level)
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
fp_sq = averaged_fplus_sq_approximated(fr, len_arm)
s_acc_nu, s_oms_nu = taiji_psd_components(
fr, acc_noise_level, oms_noise_level)
omega_len = omega_length(fr, len_arm)
sense_curve = ((s_oms_nu + s_acc_nu*(3+np.cos(2*omega_len))) /
(omega_len**2*fp_sq))
fseries = from_numpy_arrays(fr, sense_curve/2,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_lisa_SciRD(length, delta_f, low_freq_cutoff):
""" The analytical LISA's sensitivity curve in SciRD,
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged analytical
LISA's sensitivity curve in SciRD.
Notes
-----
Please see Eq.(114) in <LISA-LCST-SGS-TN-001> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
s_I = 5.76e-48 * (1+(4e-4/fr)**2)
s_II = 3.6e-41
R = 1 + (fr/2.5e-2)**2
sense_curve = 10/3 * (s_I/(2*np.pi*fr)**4+s_II) * R
fseries = from_numpy_arrays(fr, sense_curve, length,
delta_f, low_freq_cutoff)
return fseries
[docs]def confusion_fit_lisa(length, delta_f, low_freq_cutoff, duration=1.0):
""" The LISA's sensitivity curve for Galactic confusion noise,
averaged over sky and polarization angle. No instrumental noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
duration : float
The duration of observation, between 0 and 10, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
LISA's sensitivity curve for Galactic confusion noise.
No instrumental noise.
Notes
-----
Please see Eq.(85-86) in <LISA-LCST-SGS-TN-001> for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
f1 = 10**(-0.25*np.log10(duration)-2.7)
fk = 10**(-0.27*np.log10(duration)-2.47)
sh_confusion = (0.5*1.14e-44*fr**(-7/3)*np.exp(-(fr/f1)**1.8) *
(1.0+np.tanh((fk-fr)/0.31e-3)))
fseries = from_numpy_arrays(fr, sh_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def confusion_fit_tianqin(length, delta_f, low_freq_cutoff, duration=1.0):
""" The TianQin's sensitivity curve for Galactic confusion noise,
averaged over sky and polarization angle. No instrumental noise.
Only valid for 0.5 mHz < f < 10 mHz. Note that the results between
0.5, 1, 2, 4, and 5 years are extrapolated, might be non-physical.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
duration : float
The duration of observation, between 0 and 5, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
TianQin's sensitivity curve for Galactic confusion noise.
No instrumental noise.
Notes
-----
Please see Table(II) in <10.1103/PhysRevD.102.063021>
for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
t_obs = [0.5, 1, 2, 4, 5]
a0 = [-18.6, -18.6, -18.6, -18.6, -18.6]
a1 = [-1.22, -1.13, -1.45, -1.43, -1.51]
a2 = [0.009, -0.945, 0.315, -0.687, -0.710]
a3 = [-1.87, -1.02, -1.19, 0.24, -1.13]
a4 = [0.65, 4.05, -4.48, -0.15, -0.83]
a5 = [3.6, -4.5, 10.8, -1.8, 13.2]
a6 = [-4.6, -0.5, -9.4, -3.2, -19.1]
fit_a0 = interp1d(t_obs, a0, kind='cubic', fill_value="extrapolate")
fit_a1 = interp1d(t_obs, a1, kind='cubic', fill_value="extrapolate")
fit_a2 = interp1d(t_obs, a2, kind='cubic', fill_value="extrapolate")
fit_a3 = interp1d(t_obs, a3, kind='cubic', fill_value="extrapolate")
fit_a4 = interp1d(t_obs, a4, kind='cubic', fill_value="extrapolate")
fit_a5 = interp1d(t_obs, a5, kind='cubic', fill_value="extrapolate")
fit_a6 = interp1d(t_obs, a6, kind='cubic', fill_value="extrapolate")
if duration not in t_obs:
raise Warning("Note that the results between " +
"0.5, 1, 2, 4, and 5 years are extrapolated, " +
"might be non-physical.")
# 10/3 is the factor for sky-average, the original fit in the paper
# is not sky-averaged.
sh_confusion = 10./3 * np.power(
10,
fit_a0(duration) +
fit_a1(duration) * np.log10(fr*1e3) +
fit_a2(duration) * np.log10(fr*1e3)**2 +
fit_a3(duration) * np.log10(fr*1e3)**3 +
fit_a4(duration) * np.log10(fr*1e3)**4 +
fit_a5(duration) * np.log10(fr*1e3)**5 +
fit_a6(duration) * np.log10(fr*1e3)**6
)**2
# avoid the jump of values
sh_confusion[(fr > 3e-4) & (fr < 5e-4)] = \
sh_confusion[(np.abs(fr - 5e-4)).argmin()]
sh_confusion[(fr < 3e-4) | (fr > 1e-2)] = 0
fseries = from_numpy_arrays(fr, sh_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def confusion_fit_taiji(length, delta_f, low_freq_cutoff, duration=1.0):
""" The Taiji's sensitivity curve for Galactic confusion noise,
averaged over sky and polarization angle. No instrumental noise.
Only valid for 0.1 mHz < f < 10 mHz. Note that the results between
0.5, 1, 2, and 4 years are extrapolated, might be non-physical.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
duration : float
The duration of observation, between 0 and 4, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
Taiji's sensitivity curve for Galactic confusion noise.
No instrumental noise.
Notes
-----
Please see Eq.(6) and Table(I) in <10.1103/PhysRevD.107.064021>
for more details.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
t_obs = [0.5, 1, 2, 4]
a0 = [-85.3498, -85.4336, -85.3919, -85.5448]
a1 = [-2.64899, -2.46276, -2.69735, -3.23671]
a2 = [-0.0699707, -0.183175, -0.749294, -1.64187]
a3 = [-0.478447, -0.884147, -1.15302, -1.14711]
a4 = [-0.334821, -0.427176, -0.302761, 0.0325887]
a5 = [0.0658353, 0.128666, 0.175521, 0.187854]
fit_a0 = interp1d(t_obs, a0, kind='cubic', fill_value="extrapolate")
fit_a1 = interp1d(t_obs, a1, kind='cubic', fill_value="extrapolate")
fit_a2 = interp1d(t_obs, a2, kind='cubic', fill_value="extrapolate")
fit_a3 = interp1d(t_obs, a3, kind='cubic', fill_value="extrapolate")
fit_a4 = interp1d(t_obs, a4, kind='cubic', fill_value="extrapolate")
fit_a5 = interp1d(t_obs, a5, kind='cubic', fill_value="extrapolate")
if duration not in t_obs:
raise Warning("Note that the results between " +
"0.5, 1, 2, and 4 years are extrapolated, " +
"might be non-physical.")
sh_confusion = np.exp(
fit_a0(duration) +
fit_a1(duration) * np.log(fr*1e3) +
fit_a2(duration) * np.log(fr*1e3)**2 +
fit_a3(duration) * np.log(fr*1e3)**3 +
fit_a4(duration) * np.log(fr*1e3)**4 +
fit_a5(duration) * np.log(fr*1e3)**5
)
sh_confusion[(fr < 1e-4) | (fr > 1e-2)] = 0
fseries = from_numpy_arrays(fr, sh_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_lisa_confusion(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12,
base_model="semi", duration=1.0):
""" The LISA's sensitivity curve with Galactic confusion noise,
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
base_model : string
The base model of sensitivity curve, chosen from "semi" or "SciRD".
duration : float
The duration of observation, between 0 and 10, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
LISA's sensitivity curve with Galactic confusion noise.
Notes
-----
Please see Eq.(85-86) in <LISA-LCST-SGS-TN-001> for more details.
"""
if base_model == "semi":
base_curve = sensitivity_curve_lisa_semi_analytical(
length, delta_f, low_freq_cutoff,
len_arm, acc_noise_level, oms_noise_level)
elif base_model == "SciRD":
base_curve = sensitivity_curve_lisa_SciRD(
length, delta_f, low_freq_cutoff)
else:
raise ValueError("Must choose from 'semi' or 'SciRD'.")
if duration < 0 or duration > 10:
raise ValueError("Must between 0 and 10.")
fseries_confusion = confusion_fit_lisa(
length, delta_f, low_freq_cutoff, duration)
fseries = from_numpy_arrays(base_curve.sample_frequencies,
base_curve+fseries_confusion,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_tianqin_confusion(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12, duration=1.0):
""" The TianQin's sensitivity curve with Galactic confusion noise,
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
duration : float
The duration of observation, between 0 and 5, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
TianQin's sensitivity curve with Galactic confusion noise.
"""
base_curve = sensitivity_curve_tianqin_analytical(
length, delta_f, low_freq_cutoff,
len_arm, acc_noise_level, oms_noise_level)
if duration < 0 or duration > 5:
raise ValueError("Must between 0 and 5.")
fseries_confusion = confusion_fit_tianqin(
length, delta_f, low_freq_cutoff, duration)
fseries = from_numpy_arrays(base_curve.sample_frequencies,
base_curve+fseries_confusion,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def sensitivity_curve_taiji_confusion(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12, duration=1.0):
""" The Taiji's sensitivity curve with Galactic confusion noise,
averaged over sky and polarization angle.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
duration : float
The duration of observation, between 0 and 4, in the unit of years.
Returns
-------
fseries : FrequencySeries
The sky and polarization angle averaged
Taiji's sensitivity curve with Galactic confusion noise.
"""
base_curve = sensitivity_curve_taiji_analytical(
length, delta_f, low_freq_cutoff,
len_arm, acc_noise_level, oms_noise_level)
if duration < 0 or duration > 4:
raise ValueError("Must between 0 and 4.")
fseries_confusion = confusion_fit_taiji(
length, delta_f, low_freq_cutoff, duration)
fseries = from_numpy_arrays(base_curve.sample_frequencies,
base_curve+fseries_confusion,
length, delta_f, low_freq_cutoff)
return fseries
[docs]def semi_analytical_psd_lisa_confusion_noise(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, duration=1.0,
tdi=None):
""" The TDI-1.5/2.0 PSD (X,Y,Z channel) for LISA Galactic confusion noise,
no instrumental noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
duration : float
The duration of observation, between 0 and 10, in the unit of years.
tdi : string
The version of TDI, currently only for 1.5 or 2.0.
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for LISA Galactic confusion
noise, no instrumental noise.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
if str(tdi) in ["1.5", "2.0"]:
response = averaged_response_lisa_tdi(fr, len_arm, tdi)
else:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
fseries_response = from_numpy_arrays(fr, np.array(response),
length, delta_f, low_freq_cutoff)
fseries_confusion = confusion_fit_lisa(
length, delta_f, low_freq_cutoff, duration)
psd_confusion = 2*fseries_confusion.data * fseries_response.data
fseries = from_numpy_arrays(fseries_confusion.sample_frequencies,
psd_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def analytical_psd_tianqin_confusion_noise(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
duration=1.0, tdi=None):
""" The TDI-1.5/2.0 PSD (X,Y,Z channel) for TianQin Galactic confusion
noise, no instrumental noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
duration : float
The duration of observation, between 0 and 5, in the unit of years.
tdi : string
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for TianQin Galactic confusion
noise, no instrumental noise.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
if str(tdi) in ["1.5", "2.0"]:
response = averaged_response_tianqin_tdi(fr, len_arm, tdi)
else:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
fseries_response = from_numpy_arrays(fr, np.array(response),
length, delta_f, low_freq_cutoff)
fseries_confusion = confusion_fit_tianqin(
length, delta_f, low_freq_cutoff, duration)
psd_confusion = 2*fseries_confusion.data * fseries_response.data
fseries = from_numpy_arrays(fseries_confusion.sample_frequencies,
psd_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def analytical_psd_taiji_confusion_noise(length, delta_f, low_freq_cutoff,
len_arm=3e9, duration=1.0,
tdi=None):
""" The TDI-1.5/2.0 PSD (X,Y,Z channel) for Taiji Galactic confusion
noise, no instrumental noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
duration : float
The duration of observation, between 0 and 4, in the unit of years.
tdi : string
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (X,Y,Z channel) for Taiji Galactic confusion
noise, no instrumental noise.
"""
fr = np.linspace(low_freq_cutoff, (length-1)*2*delta_f, length)
if str(tdi) in ["1.5", "2.0"]:
response = averaged_response_taiji_tdi(fr, len_arm, tdi)
else:
raise ValueError("The version of TDI, currently only for 1.5 or 2.0.")
fseries_response = from_numpy_arrays(fr, np.array(response),
length, delta_f, low_freq_cutoff)
fseries_confusion = confusion_fit_taiji(
length, delta_f, low_freq_cutoff, duration)
psd_confusion = 2*fseries_confusion.data * fseries_response.data
fseries = from_numpy_arrays(fseries_confusion.sample_frequencies,
psd_confusion, length, delta_f,
low_freq_cutoff)
return fseries
[docs]def analytical_psd_lisa_tdi_AE_confusion(length, delta_f, low_freq_cutoff,
len_arm=2.5e9, acc_noise_level=3e-15,
oms_noise_level=15e-12,
duration=1.0, tdi=None):
""" The TDI-1.5/2.0 PSD (A,E channel) for LISA
with Galactic confusion noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of LISA, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
duration : float
The duration of observation, between 0 and 10, in the unit of years.
tdi : string
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (A,E channel) for LISA with Galactic confusion
noise.
"""
psd_AE = analytical_psd_lisa_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm, acc_noise_level,
oms_noise_level, tdi)
psd_X_confusion = semi_analytical_psd_lisa_confusion_noise(
length, delta_f, low_freq_cutoff,
len_arm, duration, tdi)
# S_A = S_E = S_X - S_XY, confusion noise's contribution to
# S_XY is -0.5 * psd_X_confusion, while for S_X is psd_X_confusion.
# S_T = S_X + 2*S_XY, so S_T keeps the same.
fseries = psd_AE + 1.5 * psd_X_confusion
return fseries
[docs]def analytical_psd_tianqin_tdi_AE_confusion(length, delta_f, low_freq_cutoff,
len_arm=np.sqrt(3)*1e8,
acc_noise_level=1e-15,
oms_noise_level=1e-12,
duration=1.0, tdi=None):
""" The TDI-1.5/2.0 PSD (A,E channel) for TianQin
with Galactic confusion noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of TianQin, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
duration : float
The duration of observation, between 0 and 5, in the unit of years.
tdi : string
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (A,E channel) for TianQin with Galactic confusion
noise.
"""
psd_AE = analytical_psd_tianqin_tdi_AE(length, delta_f,
low_freq_cutoff,
len_arm, acc_noise_level,
oms_noise_level, tdi)
psd_X_confusion = analytical_psd_tianqin_confusion_noise(
length, delta_f, low_freq_cutoff,
len_arm, duration, tdi)
# S_A = S_E = S_X - S_XY, confusion noise's contribution to
# S_XY is -0.5 * psd_X_confusion, while for S_X is psd_X_confusion.
# S_T = S_X + 2*S_XY, so S_T keeps the same.
fseries = psd_AE + 1.5 * psd_X_confusion
return fseries
[docs]def analytical_psd_taiji_tdi_AE_confusion(length, delta_f, low_freq_cutoff,
len_arm=3e9, acc_noise_level=3e-15,
oms_noise_level=8e-12,
duration=1.0, tdi=None):
""" The TDI-1.5/2.0 PSD (A,E channel) for Taiji
with Galactic confusion noise.
Parameters
----------
length : int
Length of output Frequencyseries.
delta_f : float
Frequency step for output FrequencySeries.
low_freq_cutoff : float
Low-frequency cutoff for output FrequencySeries.
len_arm : float
The arm length of Taiji, in the unit of "m".
acc_noise_level : float
The level of acceleration noise.
oms_noise_level : float
The level of OMS noise.
duration : float
The duration of observation, between 0 and 4, in the unit of years.
tdi : string
The version of TDI. Choose from "1.5" or "2.0".
Returns
-------
fseries : FrequencySeries
The TDI-1.5/2.0 PSD (A,E channel) for Taiji with Galactic confusion
noise.
"""
psd_AE = analytical_psd_taiji_tdi_AE(length, delta_f, low_freq_cutoff,
len_arm, acc_noise_level,
oms_noise_level, tdi)
psd_X_confusion = analytical_psd_taiji_confusion_noise(
length, delta_f, low_freq_cutoff,
len_arm, duration, tdi)
# S_A = S_E = S_X - S_XY, confusion noise's contribution to
# S_XY is -0.5 * psd_X_confusion, while for S_X is psd_X_confusion.
# S_T = S_X + 2*S_XY, so S_T keeps the same.
fseries = psd_AE + 1.5 * psd_X_confusion
return fseries